GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

THE ALGEBRA OF NONLOCAL CHARGES IN NONLINEAR SIGMA-MODELS

We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.

The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.

Further on the current algebra of WZNW models at and away from criticality

We comment on the off-critical perturbations of WZNW models by a mass term as well as by another descendent operator, when we can compare the results with further algebra obtained from the Dirac quantization of the model, in such a way that a more general class of models be included. We discover, in both cases, hidden Kac-Moody algebras obeyed by some currents in the off-critical case, which in several cases are enough to completely fix the correlation functions.

So(2,1) Lie algebra and the Green's functions for the conditionally exactly solvable potentials

The Green's functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials. © 1994 The American Physical Society.

A free relativistic anyon with canonical spin algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra {Sμ, Sν} = εμνγSγ. It is shown that it is a general consequence of these features that the Poincaré invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Ramond-ramond central charges in the supersymmetry algebra of the superstring

The free action for the massless sector of the type II superstring was recently constructed using closed Ramond-Neveo-Schwarz superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N = 2 D = 10 supersymmetry algebra with Ramond-Ramond central charges.

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

Division of labor in Ectatomma edentatum (Hymenoptera, Formicidae)

The behavioral division of labor between queens and workers of E. edentatum was investigated under laboratory conditions. Each behavioral category of both castes was described by direct observation of the ants in the colonies. The spatial position and the behavior of each individual were recorded. A colony ethogram was constructed to determine comparatively the behavioral repertory of the 2 castes. Most of the members of the colonies, including the queens, occupied the 2nd chamber, which also contained the immature stages. Forty-two behavioral categories were recorded for the workers, and 28 for the queens. The comparison of the behavioral repertory of the 2 castes revealed that ovipositing a fecundated egg is an exclusive behavior of the queens, while the workers showed 15 exclusive behaviors. Queens were never seen foraging out of the nest. Twelve behaviors were common for both castes. Polygynic colonies have only 1 female with full-developed ovaries, which is the main egg layer of the group, a feature defining the social organization of colonies of E. edentatum as a functional monogyny.

Treatment Effects Produced by Fränkel Appliance in Patients with Class II, Division 1 Malocclusion

The purpose of this investigation was to evaluate the dentoalveolar and skeletal cephalometric changes produced by the Fränkel appliance in individuals with a Class II, division 1 malocclusion. Lateral cephalograms of 44 patients of both sexes were divided in two groups of 22 each. The control group was comprised of untreated Class II children with an initial mean age of eight years and seven months who were followed without treatment for a period of 13 months. The Fränkel group had an initial mean age of nine years and was treated for a mean period of 17 months. Lateral cephalometric headfilms of each patient were obtained at the beginning and end of treatment. The Fränkel appliance produced no significant changes in maxillary growth during the evaluation period, while a statistically significant increase in mandibular length was observed. The maxillomandibular relationship improved mostly because of an increase in mandibular length. In addition, there were no statistically significant differences in the craniofacial growth direction between the Fränkel and the control group, both showing a slight downward rotation of the palatal plane. The Fränkel appliance produced a labial tipping of the lower incisors and a lingual inclination of the upper incisors as well as a significant increase in mandibular posterior dentoalveolar height. It was concluded that the main effects of the Fränkel appliance during this time period were mostly dentoalveolar with a smaller but significant skeletal mandibular effect.

Analysis of the distances covered by first division Brazilian soccer players obtained with an automatic tracking method

Methods based on visual estimation still is the most widely used analysis of the distances that is covered by soccer players during matches, and most description available in the literature were obtained using such an approach. Recently, systems based on computer vision techniques have appeared and the very first results are available for comparisons. The aim of the present study was to analyse the distances covered by Brazilian soccer players and compare the results to the European players', both data measured by automatic tracking system. Four regular Brazilian First Division Championship matches between different teams were filmed. Applying a previously developed automatic tracking system (DVideo, Campinas, Brazil), the results of 55 outline players participated in the whole game (n = 55) are presented. The results of mean distances covered, standard deviations (s) and coefficient of variation (cv) after 90 minutes were 10,012 m, s = 1,024 m and cv = 10.2%, respectively. The results of three-way ANOVA according to playing positions, showed that the distances covered by external defender (10642 ± 663 m), central midfielders (10476 ± 702 m) and external midfielders (10598 ± 890 m) were greater than forwards (9612 ± 772 m) and forwards covered greater distances than central defenders (9029 ± 860 m). The greater distances were covered in standing, walking, or jogging, 5537 ± 263 m, followed by moderate-speed running, 1731 ± 399 m; low speed running, 1615 ± 351 m; high-speed running, 691 ± 190 m and sprinting, 437 ± 171 m. Mean distance covered in the first half was 5,173 m (s = 394 m, cv = 7.6%) highly significant greater (p < 0.001) than the mean value 4,808 m (s = 375 m, cv = 7.8%) in the second half. A minute-by-minute analysis revealed that after eight minutes of the second half, player performance has already decreased and this reduction is maintained throughout the second half. ©Journal of Sports Science and Medicine (2007).

Quasiconformal mappings in octonionic algebra: A graphical and analytical comparison

In this article, we present quasiconformal mappings related to octonionic algebra. Based on the metric definition of quasiconformal mappings and using transformations of the type f(z)=zn, we compare the graphical and analytic results. © 2009 Pushpa Publishing House.